Fixed-time fault-tolerant control method for CSTR system based on composite observer

Abstract

The invention provides a composite observer-based CSTR system fixed-time fault-tolerant control method. The invention combines the composite observer with a neural network approximation technology, and for the first time applies an adaptive fixed-time instruction filtering method and a fault-tolerant control method to a continuous stirred tank reactor system to study concentration and temperature control. Compared with a finite time algorithm, the invention has better transient performance. Compared with an adaptive backstepping control method, the problem of computational complexity is reduced, and at the same time, good control of the system is ensured when a CSTR system fails. The invention can realize control of a process object, and the control method adopted in the invention has good robustness, real-time performance and stability, and can effectively improve the dynamic characteristics of the continuous stirred tank reactor system and improve economic benefits.

Description

Technical Field

[0001] The invention relates to the field of chemical industry automatic control, and in particular to a fixed-time fault-tolerant control method for a CSTR system based on a composite observer. Background Art

[0002] Continuous Stirred-Tank Reactor (CSTR) is a chemical reactor with strong nonlinearity. Most of its control algorithms are complex and have relatively poor robustness and real-time performance. Based on this, the study of the control method of the CSTR system obviously has very important theoretical value and practical significance. For a CSTR system, the temperature in the kettle is one of the important parameters to measure its performance. In actual production, the temperature in the kettle usually has a great impact on the quality and output of the product, so it is one of the decisive factors.

[0003] CSTR reaction temperature is the most important control parameter in the polymerization process, and its control quality is closely related to production safety, production efficiency and economic benefits. Since most polymerization reactions are exothermic reactions, once the heat exchange system fails, it will not only reduce production efficiency, but also affect the operational safety in the actual process. Once the CSTR temperature control fails, it may cause abnormal emergency shutdown, production suspension accidents, and even fire and explosion accidents in severe cases, resulting in loss of personnel and equipment property.

[0004] Unlike the asymptotic convergence method, the finite time control method can ensure that the tracking error converges to the equilibrium point quickly, but its setting convergence time is closely related to the initial state. Since the initial conditions in the CSTR system are mostly unknown, the setting convergence time of the fixed time control algorithm is independent of the initial value, which further solves the problem of setting convergence time under unknown initial conditions in the CSTR system.

[0005] In addition, the reaction concentration is also a factor that must be considered, which can directly reflect the reaction conditions in the kettle and the actual product quality. Therefore, real-time monitoring of reaction concentration is also an important task. However, in the actual chemical production process, real-time monitoring of concentration and temperature is very complex and expensive, and is very limited in many aspects such as detection conditions and costs. Summary of the invention

[0006] To solve the above problems, the present invention proposes a fixed-time fault-tolerant control method for a CSTR system based on a composite observer to perform real-time estimation of the system. The present invention constructs a state observer and a disturbance observer by using a composite observer to measure the unmeasurable states and disturbances in the system. The fault-tolerant controller is used to drive and maintain the state trajectory of the control system on a set submanifold within a fixed time, while still having good control when a fault occurs.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is: a fixed-time fault-tolerant control method for a CSTR system based on a composite observer, wherein the composite observer includes a state observer and a disturbance observer, which are respectively used to estimate the unmeasurable state and external disturbance in the system,

[0008] The fault-tolerant control method comprises the following steps:

[0009] Step 1: Establish a CSTR system model with disturbance based on the concentration and temperature mathematical model of the CSTR system;

[0010] Step 2: The CSTR system model established in step 1 is expressed as a state space model, and the corresponding state observer and disturbance observer are constructed to estimate the unmeasurable state and disturbance in the system, and Lyapunov stability analysis is performed with reference to the observation error system;

[0011] Step 3: According to the state space model established in step 2, design corresponding virtual control signals and adaptive laws for each subsystem;

[0012] Step 4. Based on step 3, a fault-tolerant controller is designed to make the CSTR system meet the actual fixed-time stability condition, that is, the concentration and temperature control of the CSTR system is completed.

[0013] Furthermore, step 1 specifically includes:

[0014] Step 1.1, firstly, establish the concentration and temperature mathematical model of the CSTR system according to the CSTR system structure diagram:

[0015] Assume that reactant A has a flow rate G0, temperature T0, and concentration H E0 The reactant A is added to the reactor I from the upper inlet, and the reactor I is connected to the reactor II through a pipeline. The residual reactant A is discharged from the lower outlet of the reactor II at a flow rate G2, temperature T2, and concentration H E2 Extraction; cooling water flow rate G h1 and temperature T h10 Add to the cooling jacket around reactor I at a flow rate of G h2 and temperature T h20Add to the cooling jacket around reactor II, then the cooling water flows out from the upper outlet of the cooling jacket around reactor I and reactor II, respectively, with a flow rate of G h1 and G h2 , temperature is T h1 and T h2 ;

[0016] Define the volumes of the two reactors as V = V1 = V2 and the volumes of the two cooling jackets as V = V h1 =V h2 , the flow rate of reactant A G=G0=G2,G1=G+G T , based on the mass and energy balance, the dynamic model of the CSTR system is expressed as follows:

[0017]

[0018] in represents the reaction rate constant, I represents the heat generation rate, C represents the activation energy, B represents the universal gas constant; δ and Y δ Respectively represent the density and heat capacity of the liquid in the reactor; δ h and Y h represent the density and heat capacity of the cooling water in the jacket, respectively; K represents the heat transfer coefficient between the tank reactor and the jacket, and E represents the corresponding heat transfer area;

[0019] To facilitate the study, we define x 1，2 =j2, in and is the steady-state value, therefore, the dynamic model of the CSTR system can be described as:

[0020]

[0021] Where L 1，1 =L 1，2 =1,

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032] Step 1.2, establish a perturbation d m，i =0.1sin(t)(1≤m≤3, 1≤i≤2) is a nonlinear system for concentration and temperature control of the CSTR system. The mathematical model can be expressed as follows:

[0033]

[0034] Furthermore, step 2 specifically includes:

[0035] Step 2.1, the nonlinear model of the CSTR system is expressed as the following state space model:

[0036]

[0037] Where: x m =[x m，1 , ..., x m，i ] T , f 1，1 (x m )=0,ψ m，i =d m，i +Δf m，i , f 1，2 (x m )=0, They are all sufficiently smooth nonlinear functions;

[0038] Step 2.2, construct the following state observer to estimate the unmeasurable state:

[0039]

[0040] in, is a strict Hurwitz matrix, there exists a positive definite matrix Q m =Q m T >0,P m =P m T >0, and satisfies A m T P m +Pm A m =-Q m ;

[0041] definition Then the state error system can be obtained as:

[0042]

[0043] in

[0044]

[0045] Step 2.3, construct the following auxiliary function:

[0046] e m，i =ψ m，i -r m，i x m，i , i=1,2,...,n m ;

[0047] where r m，i >0 is a design parameter, and the derivative of the above formula yields:

[0048]

[0049] where i = 1, 2, ..., n m -1;

[0050] The estimation system of the auxiliary function is expressed as:

[0051]

[0052] The following disturbance observer is constructed to estimate the external unmeasurable disturbance:

[0053]

[0054] definition Then the disturbance error system can be obtained as:

[0055]

[0056] Step 2.4, construct Lyapunov function

[0057] V m，0 The derivative is

[0058]

[0059] where a m，0 >0 is the design parameter,

[0060] Furthermore, step 3 specifically includes:

[0061] Step 3.1, define the following coordinate transformation:

[0062]

[0063] where z m，i is the error surface, y mr is the reference signal, α m，i-1 is the virtual control signal, is the output of the first-order filter;

[0064] Step 3.2, construct the following first-order filter:

[0065]

[0066] where β m，i represents a time constant;

[0067] The compensation error signal is defined as follows:

[0068]

[0069] in is the compensation error signal, η m，i is the error compensation signal;

[0070] The following error compensation mechanism is introduced to solve the filtering error Impact:

[0071]

[0072] where η m，i (0) = 0, l m，i1 >0,l m，i2 >0 is the design parameter;

[0073] Step 3.3, combining the state space model of the CSTR system in step 2 with the coordinate transformation, we can obtain:

[0074]

[0075] Introduce the error compensation signal of the above formula We can get:

[0076]

[0077] Constructing Lyapunov functions in is the parameter estimation error,

[0078] V m，1 The derivative is:

[0079]

[0080] Using RBF neural network to approximate unknown nonlinear functions And through Young's inequality processing, we can get:

[0081]

[0082]

[0083]

[0084] where |ε m，1 |≤δ m，1 ;

[0085] Substituting the above formula into the equation, we can get:

[0086]

[0087] Design the following virtual control signal:

[0088]

[0089] Parameter Adaptive Law

[0090]

[0091] where k m，11 , k m，12 , a m，1 , c m，1 , All are design parameters;

[0092] Substituting the virtual control signal and parameter adaptation law into the equation, we can obtain:

[0093]

[0094] where λ m，1 =λ m，0 -(1 / 2), b m，1 =b m，0 -(1 / 2);

[0095]

[0096] Step 3.4, combining the state space model of the CSTR system in step 2 with the coordinate transformation, we can obtain:

[0097]

[0098] Introduce error compensation signal to solve the impact of filtering error:

[0099]

[0100] Construct a Lyapunov function:

[0101]

[0102] Taking its derivative we get:

[0103]

[0104] Using Young's inequality, we can get:

[0105]

[0106] Furthermore, step 4 specifically includes:

[0107] Design the following fault-tolerant controller:

[0108]

[0109] in is the design parameter, is a positive design parameter;

[0110] Substituting the above formula into

[0111]

[0112] in

[0113] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention combines a composite observer with a neural network approximation technology, and for the first time applies an adaptive fixed-time instruction filtering method and a fault-tolerant control method to a continuous stirred tank reactor system to study concentration and temperature control; compared with a finite time algorithm, the present invention has better transient performance; compared with an adaptive backstepping control method, the problem of computational complexity is reduced, and at the same time, good control of the system is ensured even when a CSTR system fails; the present invention can be used to control a process object, and the control method used in the present invention has good robustness, real-time performance and stability, and can effectively improve the dynamic characteristics of a continuous stirred tank reactor system and improve economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0114] Figure 1 It is a schematic diagram of the structure of the CSTR system;

[0115] Figure 2 It is a flow chart of the CSTR system design scheme;

[0116] Figure 3 It is the simulation result of the CSTR system output signal, state observation signal and reference signal;

[0117] Figure 4 is the simulation result of the tracking error of the CSTR system;

[0118] Figure 5 It is the simulation result of external disturbance and disturbance observation signal of CSTR system;

[0119] Figure 6 is the simulation result of the control input of the CSTR system. DETAILED DESCRIPTION

[0120] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0121] A fixed-time fault-tolerant control method based on a composite observer, such as Figure 2 As shown, the following steps are included:

[0122] Step 1: Establish a CSTR system model with disturbance based on the concentration and temperature mathematical model of the CSTR system;

[0123] Step 2: The CSTR system model with disturbance established in step 1 is expressed as a state space model, and the corresponding state observer and disturbance observer are constructed to estimate the unmeasurable state and disturbance in the system, and Lyapunov stability analysis is performed with reference to the observation error system;

[0124] Step 3: According to the state space model of the CSTR system with disturbance established in step 2, design corresponding virtual control signals and adaptive laws for each subsystem;

[0125] Step 4: Based on step 3, a fault-tolerant controller is designed so that the CSTR system meets the actual fixed-time stability condition, that is, the concentration and temperature control of the CSTR system is completed;

[0126] The following is a detailed description of the technical solutions for each step:

[0127] Step 1: Based on the concentration and temperature mathematical model of the CSTR system, a CSTR system model with disturbance is established, which specifically includes:

[0128] Step 1.1, such as Figure 1The diagram shows the structure of the CSTR system. First, according to the CSTR system structure diagram, the process of establishing the concentration and temperature mathematical model of the CSTR system is as follows:

[0129] In the two reactors connected to each other, there is a first-order chemical reaction, Ⅰ→Ⅱ, which is irreversible and exothermic. In order to stabilize the temperature of the tank reactor at a reference constant value, cooling jackets are designed around the two reactors. Reactant A is heated at flow rate G0, temperature T0, concentration H E0 From the upper inlet, add to reactor I. Because reactor I is connected to II through a pipeline, the remaining reactant A can be added from the lower outlet of reactor II at a flow rate G2, temperature T2, concentration H E2 Extraction. Cooling water at flow rate G h1 and temperature T h10 Add to the cooling jacket around reactor I at a flow rate of G h2 and temperature T h20 Then, cooling water flows out from the upper outlet of the cooling jackets around reactors I and II, respectively, with a flow rate of G h1 and G h2 , temperature is T h1 and T h2 Assume that the volumes of the two reactors are V = V1 = V2 and the volumes of the two cooling jackets are V = V h1 =V h2 , the flow rate of reactant A G=G0=G2,G1=G+G T On the basis of mass and energy balance, the dynamic model of the CSTR system is expressed as follows:

[0130]

[0131] in represents the reaction rate constant, I represents the heat generation rate, C represents the activation energy, B represents the universal gas constant; δ and Y δ Represent the density and heat capacity of the liquid in the reactor respectively. h and Y h represent the density and heat capacity of the cooling water in the jacket, respectively; K represents the heat transfer coefficient between the tank-reactor and the jacket, and E represents the corresponding heat transfer area. The basic control objective is to manipulate H E2 , T1 and T2 to achieve appropriate H E0 、T h10 and T h20 .

[0132] To facilitate the study, we define x 1，2 =j2, in and is the steady-state value, therefore, the dynamic model of the CSTR system can be described as:

[0133]

[0134] Where L 1，1 =L 1，2 =1,

[0135]

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145] In this embodiment:

[0146]

[0147]

[0148] Step 1.2, establish a perturbation d m，i =0.1sin(t)(1≤m≤3, 1≤i≤2) is a nonlinear system for concentration and temperature control of the CSTR system. The mathematical model can be expressed as follows:

[0149]

[0150] Step 2: Based on the CSTR system model with disturbance established in step 1, construct the corresponding state observer and disturbance observer to estimate the unmeasurable state and disturbance in the system, and perform Lyapunov stability analysis with reference to the observation error system, including:

[0151] Step 2.1, the nonlinear model of the CSTR system is expressed as the following state space model:

[0152]

[0153] Where: x m =[x m，1 , ..., x m，i ] T , f 1，1 (x m )=0,ψ m，i =d m，i +Δf m，i , They are all sufficiently smooth nonlinear functions;

[0154] Step 2.2, construct the following state observer to estimate the unmeasurable state:

[0155]

[0156] in is a strict Hurwitz matrix, there exists a positive definite matrix Q m =Q m T >0,P m =P m T >0, and satisfies A m TP m +P m A m =-Q m ;

[0157] By definition Then the state error system can be obtained as:

[0158]

[0159] in

[0160]

[0161] Step 2.3, construct the following auxiliary function:

[0162] e m，i =ψ m，i -r m，i x m，i , i=1,2,...,n m ;

[0163] where r m，i >0 is a design parameter, and the derivative of the above formula yields:

[0164]

[0165] where i = 1, 2, ..., n m -1;

[0166] The estimation system of the auxiliary function is expressed as

[0167]

[0168] The following disturbance observer is constructed to estimate the external unmeasurable disturbance:

[0169]

[0170] definition Then the disturbance error system can be obtained as:

[0171]

[0172] Step 2.4, construct Lyapunov function

[0173] V m，0 The derivative is

[0174]

[0175] The above nonlinear function is approximated by using radial basis neural networks (RBFNNs): where ε m，i0 represents the minimum approximation error, where is the parameter estimation error,

[0176] Given Young's inequality and neural network basis functions We can get:

[0177]

[0178]

[0179]

[0180]

[0181]

[0182] in |ε m，i0 |≤δ m，i0 ;

[0183] Substituting the above inequality into We can get:

[0184]

[0185] where a m，0 >0 is the design parameter,

[0186] Step 3: Based on the state space model of the CSTR system with disturbance established in step 1, design corresponding virtual control signals and adaptive laws for each subsystem, specifically including:

[0187] Step 3.1, define the following coordinate transformation:

[0188]

[0189] where z m，i is the error surface, y mr is the reference signal, α m，i-1 is the virtual control signal, is the output of the first-order filter;

[0190] Step 3.2, construct the following first-order filter:

[0191]

[0192] where β m，i represents a time constant;

[0193] The compensation error signal is defined as follows:

[0194]

[0195] in is the compensation error signal, η m，i is the error compensation signal;

[0196] The following error compensation mechanism is introduced to solve the filtering error Impact:

[0197]

[0198] where η m，i (0) = 0, l m，i1 >0,l m，i2 >0 is the design parameter;

[0199] Step 3.3, combining the state space model of the CSTR system in step 2 with the coordinate transformation, we can obtain:

[0200]

[0201] Introduce the error compensation signal of the above formula We can get:

[0202]

[0203] Constructing Lyapunov functions in is the parameter estimation error,

[0204] V m，1 The derivative is:

[0205]

[0206] Using RBF neural network to approximate unknown nonlinear functions And through Young's inequality processing, we can get:

[0207]

[0208]

[0209]

[0210] where |ε m，1 |≤δ m，1 ;

[0211] Substituting the above formula into the equation, we can get:

[0212]

[0213] Design the following virtual control signal:

[0214]

[0215] Parameter Adaptive Law

[0216]

[0217] where k m，11 , k m，12 , a m，1 , c m，1 , All are design parameters;

[0218] Substituting the virtual control signal and parameter adaptation law into the equation, we can obtain:

[0219]

[0220] where λ m，1 =λ m，0 -(1 / 2), b m，1 =b m，0 -(1 / 2);

[0221]

[0222] Step 3.4, combining the state space model of the CSTR system in step 2 with the coordinate transformation, we can obtain:

[0223]

[0224] Introduce error compensation signal to solve the impact of filtering error:

[0225]

[0226] Construct a Lyapunov function:

[0227]

[0228] Taking its derivative we get:

[0229]

[0230] Using Young's inequality, we can get:

[0231]

[0232] Step 4: Based on step 3, a fault-tolerant controller is designed to make the CSTR system meet the actual fixed time stability condition, that is, the concentration and temperature control of the CSTR system is completed, specifically including:

[0233] Design the following fault-tolerant controller:

[0234]

[0235] in is the design parameter, is a positive design parameter;

[0236] Substituting the above formula into

[0237]

[0238] Given that

[0239]

[0240] Substituting the above formula into

[0241]

[0242] Lemma 1: x1, y2 represent arbitrary variables, k1, k2, B represent arbitrary constants,

[0243]

[0244]

[0245] Here ι1=0.11;

[0246] definition

[0247] Based on Lemma 2:

[0248]

[0249]

[0250] Based on Lemma 3: H n ∈R, i=1,...,n, κ∈[0,1]

[0251] (|H1|+…+|H n |) κ ≤|H1| κ +…+|H n | κ

[0252]

[0253] Substitute the above formula into We can get:

[0254]

[0255] in

[0256] Based on the following Lemma 5: satisfy 0<α<1,β>1,ω i >1,

[0257]

[0258]

[0259] Substitute the above formula into Available

[0260]

[0261] in

[0262] based on and are eliminated by the following Young's inequality:

[0263]

[0264] Substituting the above formula into It can be expressed as:

[0265]

[0266] In the formula

[0267] According to Lemmas 2 and 3, It can be expressed as:

[0268]

[0269] in

[0270]

[0271] According to Lemma 6: If V(x) is a positive definite function, and has the following form

[0272]

[0273] Wherein φ1, φ2, α, β, γ all represent normal numbers, and simultaneously satisfy αγ∈(0,1), βγ∈(1,∞), ρ>0.

[0274] It can be proved that the origin of the system has reached practical fixed-time stability (compared with asymptotic stability or finite-time stability, the practical fixed-time stability chosen in this paper has the advantage that the convergence time can be predicted normally without considering the initial conditions).

[0275] After consulting existing literature, the parameters are selected as follows β=2,γ=1 is more convenient for practical design.

[0276] The above is a specific implementation scheme of the embodiment of the present invention. The present invention simulates the control system through Matlab and analyzes its stability and real-time performance. It can be obtained that the CSTR system meets the actual fixed time stability condition.

[0277] The design goal of this application is to design a fault-tolerant controller v m，0 , so that the output signal y m Tracking reference signal y mr , and ensures that the tracking error z m,1 In a small neighborhood that converges to zero within a fixed time interval; the simulation results of the CSTR system output signal, state observation signal and reference signal are as follows Figure 3 The tracking error simulation results of the CSTR system are shown in Figure 4 The simulation results of the external disturbance and disturbance observation signal of the CSTR system are shown in Figure 5 The simulation results of the control input of the CSTR system are shown in Figure 6In summary, the present invention can measure the unmeasurable state and disturbance in the system by using a composite observer to construct a state observer and a disturbance observer.

[0278] This application combines a composite observer with a neural network approximation technique, and for the first time applies an adaptive fixed-time command filtering method and a fault-tolerant control method to a continuous stirred tank reactor system to study concentration and temperature control. Compared with a finite-time algorithm, the present invention has better transient performance; compared with an adaptive backstepping control method, it reduces the problem of computational complexity, while ensuring that the system is still well controlled when a CSTR system fails. The present invention can be used to control process objects, and the control method used in the present invention has good robustness, real-time performance, and stability, and can effectively improve the dynamic characteristics of a continuous stirred tank reactor system and improve economic efficiency.

[0279] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A fixed-time fault-tolerant control method for a CSTR system based on a composite observer, wherein the composite observer includes a state observer and a disturbance observer, which are used to estimate the unmeasurable state and external disturbance in the system, respectively, and is characterized in that: The fault-tolerant control method comprises the following steps: Step 1: Establish a CSTR system model with disturbance based on the concentration and temperature mathematical model of the CSTR system; Step 2: The CSTR system model established in step 1 is expressed as a state space model, and the corresponding state observer and disturbance observer are constructed to estimate the unmeasurable state and disturbance in the system, and Lyapunov stability analysis is performed with reference to the observation error system; Step 3: According to the state space model established in step 2, design corresponding virtual control signals and adaptive laws for each subsystem; Step 4: Based on step 3, a fault-tolerant controller is designed so that the CSTR system meets the actual fixed-time stability condition, that is, the concentration and temperature control of the CSTR system is completed; Step 3 specifically includes: Step 3.1, define the following coordinate transformation: where z m，i is the error surface, y mr is the reference signal, α m，i-1 is the virtual control signal, is the output of the first-order filter; Step 3.2, construct the following first-order filter: where β m，i represents a time constant; The compensation error signal is defined as follows: in is the compensation error signal, η m，i is the error compensation signal; The following error compensation mechanism is introduced to solve the filtering error Impact: where η m，i (0) = 0, l m，i1 >0,l m，i2 >0 is the design parameter; Step 3.3, combining the state space model of the CSTR system in step 2 with the coordinate transformation, we can obtain: Introduce the error compensation signal of the above formula We can get: Constructing Lyapunov functions in is the parameter estimation error, V m，1 The derivative is: Using RBF neural network to approximate unknown nonlinear functions And through Young's inequality, we can get: where |ε m，i |≤δ m，1 ; Substituting the above formula into the equation, we can get: Design the following virtual control signal: Parameter Adaptive Law where k m，11 , k m，12 , a m，1 , c m，1 , All are design parameters; Substituting the virtual control signal and parameter adaptation law into the equation, we can obtain: among them m，1 =λ m，0 -(1 / 2),b m，1 =b m，0 -(1 / 2); Step 3.4, combining the state space model of the CSTR system in step 2 with the coordinate transformation, we can obtain: Introduce error compensation signal to solve the impact of filtering error: Construct a Lyapunov function: Taking its derivative we get: Using Young's inequality, we can get: Step 4 specifically includes: Design the following fault-tolerant controller: in is the design parameter, is a positive design parameter; Substituting the above formula into in 2. The fixed-time fault-tolerant control method for a CSTR system based on a composite observer according to claim 1 is characterized in that: Step 1 specifically includes: Step 1.1, firstly, establish the concentration and temperature mathematical model of the CSTR system according to the CSTR system structure diagram: Assume that reactant A has a flow rate G0, temperature T0, and concentration H E0 The reactant A is added to the reactor I from the upper inlet, and the reactor I is connected to the reactor II through a pipeline. The residual reactant A is discharged from the lower outlet of the reactor II at a flow rate G2, temperature T2, and concentration H E2 Extraction; cooling water flow rate G h1 and temperature T h10 Add to the cooling jacket around reactor I at a flow rate of G h2 and temperature T h20 Add to the cooling jacket around reactor II, then the cooling water flows out from the upper outlet of the cooling jacket around reactor I and reactor II, respectively, with a flow rate of G h1 and G h2 , temperature is T h1 and T h2 ; Define the volumes of the two reactors as V = V1 = V2 and the volumes of the two cooling jackets as V = V h1 =V h2 , the flow rate of reactant A G=G0=G2,G1=G+G T , based on the mass and energy balance, the dynamic model of the CSTR system is expressed as follows: in represents the reaction rate constant, I represents the heat generation rate, C represents the activation energy, B represents the universal gas constant; δ and Y δ Respectively represent the density and heat capacity of the liquid in the reactor; δ h and Y h represent the density and heat capacity of the cooling water in the jacket, respectively; K represents the heat transfer coefficient between the tank reactor and the jacket, and E represents the corresponding heat transfer area; To facilitate the study, we define x 1，2 =j2, x 3，1 =T1-T1 c , in T1 c , and is the steady-state value, therefore, the dynamic model of the CSTR system can be described as: Where L 1，1 =1 1,2 =1, Step 1.2, establish a perturbation d m，i =0.1sin(t)(1≤m≤3, 1≤i≤2) is a nonlinear system for concentration and temperature control of the CSTR system. The mathematical model can be expressed as follows:

3. The fixed-time fault-tolerant control method for a CSTR system based on a composite observer according to claim 2 is characterized in that: Step 2 specifically includes: Step 2.1, the nonlinear model of the CSTR system is expressed as the following state space model: Where: x m =[x m , 1, ..., x m，i ] T , f 1，1 (x m )=0,ψ m，i =d m，i +Δf m，i , f 1，2 (x m )=0 , are all sufficiently smooth nonlinear functions; Step 2.2, construct the following state observer to estimate the unmeasurable state: in, is a strict Hurwitz matrix, there exists a positive definite matrix Q m =Q m T >0,P m =P m T >0, and satisfies A m T P m +P m A m =-Q m ; definition Then the state error system can be obtained as: in Step 2.3, construct the following auxiliary function: e m，i =ψ m，i -r m，i x m，i ,i=1,2,...,n m ; where r m，i >0 is a design parameter, and the derivative of the above formula yields: where i = 1, 2, ..., n m -1; The estimation system of the auxiliary function is expressed as: The following disturbance observer is constructed to estimate the external unmeasurable disturbance: definition Then the disturbance error system can be obtained as: Step 2.4, construct Lyapunov function V m，0 The derivative is where a m，0 >0 is the design parameter,

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